"snapping" polygons together - geometry

I have a set of polygons representing administrative districts. The districts were digitized by hand, and there are small spaces between polygons where the polygons should be touching. There are probably also overlapping polygons. How can I have the polygons snap together, filling the gaps and removing overlap?
QGIS / ArcGIS or Python library solution preferred (but algorithm suggestions welcome)

I know this post is 6 months old but ayway, you can use the Integrate tool in ArcGIS which should do what you want.

Old school ArcInfo had a "clean" function - I think they did the same thing in geoprocessing if you use a geodb. In that function you set a tolerance for snapping lines and points together. The clean gets rid of all those slivers (the technical term for what you are talking about).
For Qgis:
This thread should be of some help to you
http://hub.qgis.org/issues/3126

You can find a tool in the ArcGIS world called: geometry repair. You can use the python API.

Related

VTK alternatives

I apologize if the answer was already somewhere, searching the interwebs did not return me the answer(s) I was looking for.
Situation : I have a small graph (a set of Edges and Nodes that is) - Now I want to display it in an interactive manner, and I would like to manipulate the display styles and symbols that are used for edges and nodes, programetically.
Hence kgraphviewer wont work - i want to do it programetically as stated.
I noticed VTK, comes with a lot of built is graph drawing algorithms. But seems to be a really large one.
Question : What are some alternatives to VTK ? Graphviz is probably one, but I can not confirm that graphviz comes with all the graph drawing algorithms as VTK - any other possibly smaller options, with all the built in graphs?
Side note : Some systems uses a static drawign widget, i.e. once the drawing is displayed, in an widget that the system comes with, you can not interact with the drawing using your mouse. The GNU implementation of IDL, GDL, has this problem. I would Like to avoid this.
Yes, I agree with you regarding the VTK's consideration: it's a powerful toolkit but it is (maybe) too much "big", and it's not so easy to configure a working VTK environment.
I don't have a great experience in the field of graphs, but a search leads to this other StackOverflow post. I think that Prefuse, listed under the Java section, could be of some interest. C++ itself seems to have a lot of choices, listed in various answers, here. I hope that it will help.
I used Gephi public domain graph visualization software on Linux. It was a quick way to get a 3 D. Picture which can be modified with line thickness to show an edge weight - good for comm network work.

How do I connect two arcs with a line in this d3.js visual

I saw an infographic online that I wanted to use as a challenge to learn d3.js. The original infographic is here:
http://www.shah3d.com/wp-content/uploads/2012/11/IG-WWF-Dehahs.png
I've made a start here:
http://www.tips-for-excel.com/d3test/arc/arc%20test.html
You'll notice that the original has nice lines that link an arc from the bottom with an arc along the top. So far I can only think of painfully placing lots of circles to achieve this effect, hence the odd red circle currently in my visual. What would people's best methods be to replicate the original graphic? Which element would make this task easier? Arcs? Lines? I imagine I'll have to manipulate my data so that the lines go where they're meant to.
Happy to give more info if needed and thanks for taking time to read this.
There are a few existing diagrams to work off of from d3's galleries:
http://bl.ocks.org/4062006
http://bost.ocks.org/mike/uberdata/
Both use the length of the chord as the width of the stroke (initially), but you can tinker with that, for sure.
Graphically, you could use arcs, or full circles with a clip around it. As to the 'best' way to do it, that may come out of 'requirements' of how your graphic needs to behave (animation, relative arc placement, etc).
Personally, I'd go with path arcs.

How do I reduce the coordinate count of an arbitrary SVG path, without losing much or any precision?

I am scouring the web for tools, programs, utilities, supporting libraries and code primitives that help optimize SVGs for simplicity, space and elegance recently, to link to from the Kilobyte SVG Challenge's tools section, but have yet to find good primitives focusing on how to reduce the number of coordinates of a path, without losing much – or ideally any – precision.
Take this marker-augmented version of the Coca Cola logo, for instance (~7kb, essentially all path data) – which very clearly shows lots of promise for reducing its number of bèziers, given some tooling to do the math to come up with a path using fewer nodes, while producing essentially the same curve.
For the much simpler problem of polygons and polylines (read "all-line paths"), you can use the Douglas–Peucker or Visvalingam’s algorithm (see Mike Bostock's excellent d3 implementation of the latter) to simply remove the coordinates least affecting the path's shape until you're happy with a size-to-precision fit suiting your needs.
I am looking for the equivalent that notices where larger curve (or even arc) segments could replace lots of these redundant mid-curve coordinate stops, without lots of manual tweaking. I think some vector graphics packages (Adobe Illustrator, maybe even Inkscape?) may offer features like these (tips on how to access them welcome!) - though I would love to find scriptable tools we can recommend and offer HOWTOs of how to use from the command line, or even web apps, that squeeze out excess path filler material for people.
For reference, the Kilobyte SVG Challenge is a for-fun SVG education and advocacy stunt I have set up, recently. All non-question-topic discussion about it are best held there, and/or on its github repository linked above. Stay awesome! :)
You can use Ramer–Douglas–Peucker algorithm to simplify polylines or polygons path.

How do I create a real-time rendering window from scratch?

I've been studying 3D graphics on my own for a while now and I want to get a greater understanding of just how everything works. What I would like to do is to create a simple game without using DirectX or OpenGL. I understand most of the math I believe, but the problem I am running up against is I do not know how to get control of the pixels being displayed in a window.
How do I specify what color I want each pixel in my window to be?
I understand I will probably run into issues with buffers and image shearing and probably terrible efficiency problems, but I want to create my own program so that I could see from the very lowest level, of the high level language, how the rendering process works. I really have no idea where to start though. I've figured out how to output BMPs, but I would like to have a running program spitting out 20+ frames per second. How do I accomplish this?
You could pick a environment that allows you to fill an array with values for pixels and display it as a bitmap. This way you come closest to poking RGB values in video memory. WPF, Silverlight, HTML5/Javascript can do this. If you do not make it full screen these technologies should suffice for now.
In WPF and Silverlight, use the WriteableBitmap.
In HTML5, use the canvas
Then it is up to you to implement the logic to draw lines, circles, bezier curves, 3D projections.
This is a lot of fun and you will learn a lot.
I'm reading between the lines that you're more interested in having full control over the rendering process from a low level, rather than having a specific interest in how to achieve that on one specific platform.
If that's the case then you will probably get a good bang for your buck looking at a library like SDL which provides you with a frame buffer that you can render to directly but abstracts away a lot of the platform specifics issues. It has been around for quite a while and there are some good tutorials to give you an idea of whether it's the kind of thing you're looking for - see this tutorial and the subsequent one in the same series, which should be enough to get you up and running.
You say you want to create some kind of a rendering engine, meaning desinging you own Pipeline and matrice classes. Which you are to use to transform 3D coordinates to 2D points.
When you have got the 2D points you've been looking for. You can use say for instance on windows, you can select a brush and draw you triangle values while coloring them at the same time.
I do not know why you would need Bitmaps, but if you want to practice say Texturing you can also do that yourself although off course on a weak computer this might take your frames per second significantly.
If you aim is to understand how rendering works on the lowest level. This is with no doubt a good practice.
Jt Schwinschwiga

Polygon Triangulation with Holes

I am looking for an algorithm or library (better) to break down a polygon into triangles. I will be using these triangles in a Direct3D application. What are the best available options?
Here is what I have found so far:
Ben Discoe's notes
FIST: Fast Industrial-Strength Triangulation of Polygons
I know that CGAL provides triangulation but am not sure if it supports holes.
I would really appreciate some opinions from people with prior experience in this area.
Edit: This is a 2D polygon.
To give you some more choices of libraries out there:
Polyboolean. I never tried this one, but it looks promising: http://www.complex-a5.ru/polyboolean/index.html
General Polygon Clipper. This one works very well in practice and does triangulation as well as clipping and holes holes: http://www.cs.man.ac.uk/~toby/alan/software/
My personal recommendation: Use the tesselation from the GLU (OpenGL Utility Library). The code is rock solid, faster than GPC and generates less triangles. You don't need an initialized OpenGL-Handle or anything like this to use the lib.
If you don't like the idea to include OpenGL system libs in a DirectX application there is a solution as well: Just download the SGI OpenGL reference implementation code and lift the triangulator from it. It just uses the OpenGL-Typedef names and a hand full of enums. That's it. You can extract the code and make a stand alone lib in an hour or two.
In general my advice would be to use something that alreay works and don't start to write your own triangulation.
It is tempting to roll your own if you have read about the ear-clipping or sweep-line algorithm, but fact is that computational geometry algorithms are incredible hard to write in a way that they work stable, never crash and always return a meaningful result. Numerical roundoff errors will accumulate and kill you in the end.
I wrote a triangulation algorithm in C for the company I work with. Getting the core algorithm working took two days. Getting it working with all kinds of degenerated inputs took another two years (I wasn't working fulltime on it, but trust me - I spent more time on it than I should have).
Jonathan Shewchuk's Triangle library is phenomenal; I've used it for automating triangulation in the past. You can ask it to attempt to avoid small/narrow triangles, etc., so you come up with "good" triangulations instead of just any triangulation.
CGAL has the tool you need:
Constrained Triangulations
You can simply provide boundaries of your polygon (incuding the boundaries of the holes) as constraints (the best would be that you insert all vertices, and then specify the constraints as pairs of Vertex_handles).
You can then tag the triangles of the triangulation by any traversal algorithm: start with a triangle incident to the infinite vertex and tag it as being outside, and each time you cross a constraint, switch to the opposite tag (inside if you were previously tagging the triangles as outsider, outside if you were tagging triangles as insider before).
I have found the poly2tri library to be exactly what I needed for triangulation. It produces a much cleaner mesh than other libraries I've tried (including libtess), and it does support holes as well. It's been converted to a bunch of languages. The license is New BSD, so you can use it in any project.
Poly2tri library on Google Code
try libtess2
https://code.google.com/p/libtess2/downloads/list
based on the original SGI GLU tesselator (with liberal licensing). Solves some memory management issues around lots of small mallocs.
You can add the holes relatively easily yourself. Basically triangulate to the convex hull of the input points, as per CGAL, and then delete any triangle whose incentre lies inside any of the hole polygons (or outside any of the external boundaries). When dealing with lots of holes in a large dataset, masking techniques may be used to significantly speed this process up.
edit: A common extension to this technique is to weed weak triangles on the hull, where the longest edge or smallest internal angle exceeds a given value. This will form a better concave hull.
I have implemented a 3D polygon triangulator in C# using the ear clipping method. It is easy to use, supports holes, is numerically robust, and supports aribtrary (not self-intersecting) convex/non-convex polygons.
This is a common problem in finite element analysis. It's called "automatic mesh generation". Google found this site with links to commercial and open source software. They usually presume some kind of CAD representation of the geometry to start.
Another option (with a very flexible license) is to port the algorithm from VTK:
vtkDelaunay2D
This algorithm works fairly well. Using it directly is possible, but requires links to VTK, which may have more overhead than you want (although it has many other nice features, as well).
It supports constraints (holes/boundaries/etc), as well as triangulating a surface that isn't necessarily in the XY plane. It also supports some features I haven't seen elsewhere (see the notes on Alpha values).

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